Understanding second language acquisition

This article surveys recent work on content-and-language integrated learning (CLIL). Related to both content-based instruction and immersion education by virtue of its dual focus on language and content, CLIL is here understood as an educational model for contexts where the classroom provides the only site for learners’ interaction in the target language. That is, CLIL is about either foreign languages or lingua francas. The discussion foregrounds a prototypical CLIL context (Europe) but also refers to work done elsewhere. The first part of the discussion focuses on policy issues, describing how CLIL practice operates in a tension between grassroots decisions and higher order policymaking, an area where European multi- and plurilingual policies and the strong impact of English as a lingua franca play a particularly interesting role. The latter is, of course, of definite relevance also in other parts of the world. The second part of the article synthesizes research on learning outcomes in CLIL. Here, the absence of standardized content testing means that the main focus is on language-learning outcomes. The third section deals with classroom-based CLIL research and participants’ use of their language resources for learning and teaching, including such diverse perspectives as discourse pragmatics, speech acts, academic language functions, and genre. The final part of the article discusses theoretical underpinnings of CLIL, delineating their current state of elaboration as applied linguistic research in the area is gaining momentum.

Content-and-Language Integrated Learning: From Practice to Principles?

ONAG, as the book is commonly known, is one of those rare publications that sprang to life in a moment of creative energy and has remained influential for over a quarter of a century. Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently enjoyable guide to game theory. By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers, that includes both real numbers and ordinal numbers. These surreal numbers are applied in the author's mathematical analysis of game strategies. The additions to the Second Edition present recent developments in the area of mathematical game theory, with a concentration on surreal numbers and the additive theory of partizan games.

On numbers and games, by J. H. Conway. Pp ix, 238. £6·50. 1976. SBN 0 12 186350 6 (Academic Press)

The growing interest in Content and Language Integrated Learning (CLIL) has resulted in enthusiasm in and active pursuit of improved methods of foreign/second-language (L2) teaching in Europe. However, the definition and scope of the term CLIL both internally, as used by CLIL advocates in Europe, and externally, as compared with immersion education in and outside Europe, indicate that the core characteristics of CLIL are understood in different ways with respect to: the balance between language and content instruction, the nature of the target languages involved, instructional goals, defining characteristics of student participants, and pedagogical approaches to integrating language and content instruction. We argue further that attempts to define CLIL by distinguishing it from immersion approaches to L2 education are often misguided. The aim of this article is to examine these ambiguities and to call for clarification of the definition of CLIL. Clarification is critical if CLIL is to evolve and improve systematically and if CLIL educators are to benefit from the experiences and knowledge acquired in other educational settings.

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Critical Analysis of CLIL: Taking Stock and Looking Forward

This study investigated 481 in-service elementary teachers’ level of mathematical content knowledge, attitudes toward mathematics, beliefs about the effectiveness of inquiry-based instruction, use of inquiry-based instruction and modeled the relationship among these variables. Upper elementary teachers (grades 3–5) were found to have greater content knowledge and more positive attitudes toward mathematics than primary teachers (grades K-2). There was no difference in teachers’ beliefs about effective instruction, but primary level teachers were found to use inquiry-based instruction more frequently than upper elementary teachers. Consistent with Ernest’s [Ernest (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33] model of mathematics teaching, content knowledge, attitudes, and beliefs were all found to be related to teachers’ instructional practice. Furthermore, beliefs were found to partially mediate the effects of content knowledge and attitudes on instructional practice. Content knowledge was found to be negatively related to beliefs in the effectiveness of inquiry-based instruction and teachers’ use of inquiry-based instruction in their classrooms. However, overall, teachers with more positive attitudes toward mathematics were more likely to believe in the effectiveness of inquiry-based instruction and use it more frequently in their classroom. Teacher beliefs were found to have the strongest effect on teachers’ practice. Implications for the goals and objectives of elementary mathematics methods courses and professional development are discussed.

The relationship among elementary teachers’ content knowledge, attitudes, beliefs, and practices

This paper reports a survey of research in mathematics teacher education from 1999 to 2003 done by an international team of five mathematics educators and researchers. The survey included published research in international mathematics education journals, international handbooks of mathematics education and international mathematics education conference proceedings. Some regional sources from various parts of the world were also included. We investigated who was writing, from and in what settings, with what theoretical frameworks, and with what sorts of study designs for what core questions. We also examined the range of findings and conclusions produced in these studies. Our analysis presented here focuses on four themes that stood out from our initial investigation of almost 300 published papers, and systematically elaborated through a focused study of a 160 papers across key journals and conference proceedings in the field. From this vantage point, the paper offers a reflection on the current state of the field of mathematics teacher education research. Our aim is to stimulate discussion that can support the development of the field, not make final pronouncements about its nature. KE YW ORDS: survey of field, teacher education research, teaching

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Reflections on an emerging field: Researching mathematics teacher education

Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense components, and that several components of university algebra structure sense are analogies of high school algebra structure sense components. We present a theoretical argument for these hypotheses, with some examples. We recommend emphasizing structure sense in high school algebra in the hope of easing students’ paths in university algebra. The cooperation of the authors in the domain of structure sense originated at a scientific conference where they each presented the results of their research in their own countries: Israel and the Czech Republic. Their findings clearly show that they are dealing with similar situations, concepts, obstacles, and so on, at two different levels—high school and university. In their classrooms, high school teachers are dismayed by students’ inability to apply basic algebraic techniques in contexts different from those they have experienced. Many students who arrive in high school with excellent grades in mathematics from the junior-high school prove to be poor at algebraic manipulations. Even students who succeed well in 10th grade algebra show disappointing results later on, because of the algebra. Specifically, some students drop out of advanced mathematics in 11th grade due to an inability to apply algebraic techniques in different contexts (Hoch & Dreyfus, 2004, 2005, 2006). Similarly, university lecturers involved in training future mathematics teachers often notice their students’ difficulties in developing a deeper understanding of mathematical notions that they meet in their mathematics courses. We refer to experiences from Novotna and Stehlikova’s longitudinal observation of university students—future mathematics teachers—during the course Theoretical Arithmetic and Algebra (Novotna, Stehlikova & Hoch, 2006). Students enter the course having experience with number sets and with linear and polynomial algebra (Novotna, 2000), but they often have problems with basic algebraic concepts.

https://files.eric.ed.gov/fulltext/EJ820236.pdf

How structure sense for algebraic expressions or equations is related to structure sense for abstract algebra

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Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 1.

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Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 4.

This article presents the results of an investigation carried out across 20+ country-regions under the auspices of ICMI Study 15 into the structures, approaches and general characteristics of the mathematics preparation and development of teachers. We use a global framework provided by the larger research literature on teacher education to contextualize the findings. The article provides an analytic perspective on (a) teacher education systems’ characteristics including institutional arrangements and regulations; (b) teacher’s recruitment, selection, and credentials; (c) teacher education programs’ structure and approaches; (d) teacher educators’ characteristics; and (e) the structure and content of the curriculum. This article highlights the important differences and similarities across systems that provide mathematics education and development to teachers. This article concludes with a discussion on implications for future empirical research on mathematics teacher education.

Jarmila Novotná

Papers

Reflections on an emerging field: Researching mathematics teacher education

How structure sense for algebraic expressions or equations is related to structure sense for abstract algebra

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 1.

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (30th, Prague, Czech Republic, July 16-21, 2006). Volume 4.

The organization of the mathematics preparation and development of teachers: a report from the ICMI Study 15